Categories for the Working Mathematician (Graduate Texts in Mathematics) (Hardcover)

by Saunders Mac Lane (Author) "Category theory starts with the observation that many properties of mathematical systems can be unified and simplified by a presentation with diagrams of arrows..." (more)
Key Phrases: biproduct diagram, absolute coequalizer, arrows all functions, Mac Lane, Comp Haus (more...)

Editorial Reviews

Review
Second Edition S.M. Lane Categories for the Working Mathematician "A very useful introduction to category theory."—INTERNATIONALE MATHEMATISCHE NACHRICHTEN

Product Description
Categories for the Working Mathematician provides an array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. The book then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterized by Beck's theorem. After considering a variety of applications, the book continues with the construction and expoitation of Kan extensions. This second edition includes a number of revisions and additions, including two new chapters on topics of active interest. One is on symmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The second describes 2-categories and the higher dimensional categories which have recently come into prominence. The bibliography has also been expanded to cover some of the many other recent advances concerning categories.

Product Details

• Hardcover: 314 pages
• Publisher: Springer; 2nd edition (September 25, 1998)
• Language: English
• ISBN-10: 0387984038
• ISBN-13: 978-0387984032
• Product Dimensions: 9.2 x 6.1 x 1 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 3.9 out of 5 stars See all reviews (8 customer reviews)
• Amazon.com Sales Rank: #472,564 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

32 of 34 people found the following review helpful:

5.0 out of 5 stars One of the great books in mathematics, September 24, 2000

By	Colin McLarty (Chardon, OH USA) - See all my reviews

This book is a classic. Clearly written, drawing on a vast number of different applications and motivations for the subject. Eilenberg and Mac Lane created category theory and this book is alive with the very style of thought Mac Lane brought to it in the first place. It is obvious that Mac Lane wrote each page, and each exercise, with a view of the whole book in mind. He starts with the very basics, assuming indeed that you know nothing of category theory. He goes on to adjunctions, limits, the adjoint functor theorems, monads (triples), monoidal categories, Abelian cateories, Kan extensions, higher dimensional categories, and categorical foundations. It is a masterpiece and one of the great books in mathematics.

26 of 27 people found the following review helpful:

5.0 out of 5 stars A Classic, July 2, 2004

By	Jason Schorn "j schorn" (Spokane, WA) - See all my reviews (REAL NAME)

Well, let us think about this a little bit...You want to learn Category theory, whether for some course or just for the fun of it, and now where do you turn in order to learn the necessary concepts. If you are a mathematician and have some experience, then you turn to the masters, the originators of the given subject and read their work. Sure, being the founder of a given subject does not imply that you are a good expositor and hence are capable of revealing the necessary concepts for the beginner-allow me to inform that Mac Lane is indeed as good as an expositor as he was a mathematician. For any doubters, I point you to the only other text you should read on Category theory, namely, "Category Theory" by Horst Herrlich and compare this text with Mac Lane's. Aside from that, and with respect to the text, for most beginners or interested readers I would suggest the following outline: Read 1.1-6; 2.1-3 & 8 possibly 2.4; all of 3; as for 4 skip section 3; 5.1-5; all of 8. Then, dependent upon your desires and or focus as well as your mathematical ability, it should become obvious which of the remaining topics should be read. Finally, the only other source I would recommend for learning Category theory can be found on-line using the keyword 'Awodey'. Anyways, Enjoy and good luck.

30 of 34 people found the following review helpful:

4.0 out of 5 stars Definitely a grad text, July 22, 2001

By A Customer

This book is extraordinarily well written. It covers the necessary topics in a concise, orderly manner. HOWEVER, it presumes a substantial amount of knowledges concerning various algebraic/abstract structures in the field of mathematics. If you already have had experience with such structures, and are simply looking to understand them from a different perspective - this is the book for you. However, if you have limited knowledge with regards to advanced math (ie - grad level math) then try the book 'Arrows, Structures and Functors: The Categorical Imperative' by Manes and Arbib. This introduces the reader gradually to simple algebraic structures, monoids, groups, metric spaces, topological spaces, and the categories that can be built around them.